When a device is playing out a first media stream, the device determines a target time for beginning playout of a second media stream in place of the first media stream. The device then starts a stream-transition process that is expected to take anywhere from a minimum expected transition duration to a maximum expected transition duration, and the de vice starts the transition process in advance of the determined target time by the maximum expected transition duration, to help ensure timely starting of playout of the second media stream. Further, for an uncertainty period that extends from die minimum expected transition duration after the starting to the maximum expected transition duration after the starting, the device generates and plays a sequence of transition frames to help mask transition from the first media stream to the second media stream.
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